Higgs branch of heterotic little string theories: Hasse diagrams and generalized symmetries

We study the Higgs branches of the 6D (1, 0) little string theories that live on the world volume of NS5-branes probing an ADE-singularity in the heterotic <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>E</a:mi><a:mn>8</a:mn></a:msub><a:mo>×</a:mo><a:msub><a:mi>E</a:mi><a:mn>8</a:mn></a:msub></a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mtext>Spin</c:mtext><c:mo stretchy="false">(</c:mo><c:mn>32</c:mn><c:mo stretchy="false">)</c:mo><c:mo>/</c:mo><c:msub><c:mi mathvariant="double-struck">Z</c:mi><c:mn>2</c:mn></c:msub></c:math> string theories. On the <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:msub><h:mi>E</h:mi><h:mn>8</h:mn></h:msub><h:mo>×</h:mo><h:msub><h:mi>E</h:mi><h:mn>8</h:mn></h:msub></h:math> side, such little string theories (LSTs) are obtained via fusion of orbi-instanton SCFTs. For the <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:msup><j:mi mathvariant="double-struck">C</j:mi><j:mn>2</j:mn></j:msup><j:mo>/</j:mo><j:msub><j:mi mathvariant="double-struck">Z</j:mi><j:mi>K</j:mi></j:msub></j:math> orbifolds, we determine a magnetic quiver for the Higgs branch from the alternative type IIA brane system engineering the LST; we show that the magnetic quiver obtained in this way is the same as the Coulomb gauging of the 3D mirrors associated with the orbi-instanton building blocks. Using quiver subtraction, we determine the Hasse diagram of Higgs branch renormalization group flows between the LSTs, and we analyze how the structure constants of the generalized global symmetries vary along the edges of the Hasse diagram. From the Hasse diagram of the Higgs branch, we are immediately able to identify LSTs with the same T-duality-invariant properties, and thus propose candidate T-dual pairs. We perform a similar analysis of the Higgs branch Hasse diagram and putative T-dual families for particular <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:msub><n:mi>E</n:mi><n:mn>6</n:mn></n:msub></n:math>-orbifold LSTs by taking advantage of a duality between a rank zero orbi-instanton theory and a rank one conformal matter theory. Published by the American Physical Society 2024